On semigroups of order-preserving transformations with the same fix set
Czechoslovak Mathematical Journal, cilt.76, sa.2, ss.379-399, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 76 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.21136/cmj.2026.0504-24
- Dergi Adı: Czechoslovak Mathematical Journal
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.379-399
- Anahtar Kelimeler: (completely) isolated subsemigroup, 20M05, 20M20, generating set, order-preserving transformation, orientation-preserving, rank
- Çukurova Üniversitesi Adresli: Evet
Özet
Let On be the semigroup of all order-preserving (full) transformations on the finite chain Xn = {1,…,n} under its natural order. For a singular idempotent ξ, it is shown that On(ξ)={α∈On:αm=ξfor somem∈N} is a maximal nilpotent subsemigroup of On with zero ξ. Moreover, for a nonempty subset Y of Xn, we give a necessary and sufficient condition for the set On(Y) to be a subsemigroup. Then we find a unique minimal generating set, and so rank, of On(Y) whenever it is a subsemigroup of On. Every subset Y of Xn such that On(Y) is (completely) isolated was characterized.